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A generalized theory of transformation strains in lattices is developed which incorporates earlier analyses of both deformation twinning and martensite crystallography in addition to other new transformation mechanisms. In the formal analysis two different lattices are related by an invariant plane strain, a rotation and a further strain which characterizes the particular transformation being considered. A general solution is then obtained for the invariant plane strain in terms of this characteristic strain. The special cases of twinning shears, invariant plane transformation strains and martensite crystallography theories are examined in detail for mechanisms involving either single or double strains. In these cases the characteristic strain consists of appropriate combinations of shears, pure strains, invariant plane strains and lattice invariant deformations. Applications of the particular mechanisms examined to transformations of technological interest in crystalline materials are discussed and further special cases and extensions of the analysis considered.

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